Are you saying that you were issued with a PNR (Record Locator in AA lingo) but the booking was never ticketed?
That has happened to me in the past both via internet booking on AA’s website and bookings on the phone through an agent. I have been lucky in that, upon confirming the lapse, inventory was still available and another booking could be made.
The key here is to never rest until you receive an email from AA detailing the ticket number for your booking. If you have not received an email with your ticket details and confirmation that you have used your Aadvantage miles, I would be on the phone to AA to get it sorted. If they tell you it will happen in time, kick a fuss and tell them your booking has dropped in the past and you wish to ensure it does not occur again. At the very least, there would be a record of your interaction with AA should you require recourse in the event that things go wrong.
I know it’s not ideal but at least you save money booking online than via an agent. I know it’s frustrating when IT systems do not work as designed but I think it is folly to assume IT systems are infallible.